Question

given the following picture, the value of x = (type your answer) and y = (type your answer). (4y + 5)° (25x + 8)° (9x + 2)°

Explanation:

Step1: Use vertical - angles property

Vertical angles are equal. So, \(25x + 8=9x + 2\).

Step2: Solve for \(x\)

Subtract \(9x\) from both sides: \(25x-9x + 8=9x-9x + 2\), which simplifies to \(16x+8 = 2\). Then subtract 8 from both sides: \(16x+8 - 8=2 - 8\), getting \(16x=-6\). Divide both sides by 16: \(x=\frac{-6}{16}=-\frac{3}{8}\).

Step3: Use another pair of vertical - angles

The other pair of vertical angles gives \(4y + 5=9x + 2\). Substitute \(x =-\frac{3}{8}\) into the equation: \(4y+5=9\times(-\frac{3}{8})+2\). First, calculate \(9\times(-\frac{3}{8})=-\frac{27}{8}\), then the equation becomes \(4y + 5=-\frac{27}{8}+2\). Rewrite 2 as \(\frac{16}{8}\), so \(4y + 5=-\frac{27}{8}+\frac{16}{8}=-\frac{11}{8}\). Subtract 5 from both sides: \(4y=-\frac{11}{8}-5\). Rewrite 5 as \(\frac{40}{8}\), then \(4y=-\frac{11}{8}-\frac{40}{8}=-\frac{51}{8}\). Divide both sides by 4: \(y =-\frac{51}{32}\).

Answer:

\(x =-\frac{3}{8}\), \(y =-\frac{51}{32}\)